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Contract No. DE-AC36-08GO28308

Investigation of Thermal 

Interface Materials Using 

Phase-Sensitive Transient 

Thermoreflectance Technique

Preprint

Xuhui Feng, Charlie King, Doug DeVoto, 

Mark Mihalic, and Sreekant Narumanchi

Presented at ITherm 2014

Orlando, Florida

May 27 – 30, 2014

Conference Paper

NREL/CP-5400-61106

August 2014
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Investigation of Thermal Interface Materials Using Phase-Sensitive Transient Thermoreflectance 

Technique

Xuhui Feng, Charlie King, Doug DeVoto, Mark Mihalic, and Sreekant Narumanchi

National Renewable Energy Laboratory

Golden CO 80401

Email: xuhui.feng@nrel.gov

ABSTRACT

With increasing power density in electronics 

packages/modules, thermal resistances at multiple interfaces 

are a bottleneck to efficient heat removal from the package. In 

this work, the performance of thermal interface materials such 

as grease, thermoplastic adhesives and diffusion-bonded 

interfaces are characterized using the phase-sensitive transient 

thermoreflectance technique. A multi-layer heat conduction 

model was constructed and theoretical solutions were derived 

to obtain the relation between phase lag and the 

thermal/physical properties. This technique enables 

simultaneous extraction of the contact resistance and bulk 

thermal conductivity of the TIMs. With the measurements, the 

bulk thermal conductivity of Dow TC-5022 thermal grease (70

to 75 μm bondline thickness) was 3 to 5 W/(m·K) and the 

contact resistance was 5 to 10 mm2

·K/W. For the Btech 

thermoplastic material (45 to 80 μm bondline thickness), the 

bulk thermal conductivity was 20 to 50 W/(m·K) and the 

contact resistance was 2 to 5 mm2

·K/W. Measurements were 

also conducted to quantify the thermal performance of 

diffusion-bonded interface for power electronics applications.

Results with the diffusion-bonded sample showed that the 

interfacial thermal resistance is more than one order of 

magnitude lower than those of traditional TIMs, suggesting 

potential pathways to efficient thermal management.

KEY WORDS: Thermal interface materials, phase-sensitive 

transient thremoreflectance, contact resistance, bulk thermal 

conductivity, thermophysical properties

NOMENCLATURE

c specific heat, J/(kg·K)

d thickness, m 

f frequency, Hz

h contact conductance, W/(m2

·K)

k thermal conductivity, W/(m·K)

lp thermal penetration depth, m

q0 amplitude of laser heat flux 

r radial axis, m

R thermal resistance, m2

·K /W

t time, s

T temperature, K

z axis along thickness direction, m

Greek symbols

α thermal diffusivity (m2

/s)

ω angular frequency (radians/s)

ρ density (kg/m3

)

Subscripts

1, 2, 3 layer index in multi-layer modeling

INTRODUCTION

With increasing power density in electronics 

packages/modules, the need for efficient heat removal is 

becoming important. Thermal interface materials (TIMs) are of 

particular interest in packaging and play a key role in reducing

the thermal resistance between mating surfaces in the heat 

conduction path [1-6]. Effective TIMs reduce the package 

resistance and help maintain an appropriate working 

temperature to ensure both performance and reliability of the 

devices. To fulfill the purpose of efficient conduction of heat, 

TIMs usually are expected to possess two major characteristics: 

high thermal conductivity and good conformability to mating 

surfaces. Commercially available TIMs include thermal grease, 

gels, solders, and phase-change materials (PCMs). Significant 

amount of research has been reported regarding the synthesis, 

properties, and modifications of TIMs. Liu and Chung used 

scanning calorimetry to evaluate PCMs for use as TIMs [7].

Aoyagi et al. [8] evaluated the polyol-based PCMs, which have

thermal contact conductance higher than those of paraffin wax, 

polyether glycol, etc. Its thermal stability is superior to other

PCMs [8]. Boron nitride is used as it is more effective than 

carbon black. Aoyagi and Chung [9] reported antioxidantbased PCMs with high thermal stability. Yu et al. [10] applied 

graphite nanoplatelets as filler for epoxy composites and found 

that the thermal conductivity was enhanced with a relatively 

low volume fraction due to the filler’s high aspect ratio, twodimensional geometry, and low thermal interface resistance. In 

addition, for new nanostructured materials that may possess 

improved thermal and mechanical properties, their potential of 

being applied as TIMs is also studied. Cross et al. [11]

measured the thermal performance of dense, vertically aligned 

multi-wall carbon nanotube (MWCNT) arrays as TIMs. CNTs

were utilized as TIMs after appropriate metallization and 

bonding. The thermal resistance was measured using a 

photoacoustic technique to be in the range of 1.7 to 10 

mm2

∙K/W, depending on the vertical length of CNTs.

To experimentally characterize the thermal properties and 

thermal performance of TIMs, a variety of techniques have 

been developed and utilized, including both steady-state and 

transient techniques. Lasance[12] reviewed several urgent 

needs for developing widely accepted test methods of TIMs 

due to the substantial difference amongst TIMs. There can be 

significant discrepancies in the results obtained from the 

various techniques. But in recent years, the ASTM D-5470 [13]

has emerged as a standard based on a steady-state approach. In 

addition, a number of steady-state and transient cannot 

accurately measure thermal resistances below 1 mm2

·K/W. 

Culham et al. [14] designed a test apparatus that exceeded all 

specifications stipulated in ASTM-D5470-95 and that can be 

used to characterize TIMs. Xu and Fisher [15] tested the 

thermal conductance of silicon wafers with CNT arrays using a 
2

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one-dimensional steady-state heat conduction experiment with 

a reference calorimeter setup. Chen et al. [16] designed a 

platform based on ASTM D5470 test method to measure 

polymeric TIMs such as greases. Due to the limitations of

ASTM–D5470 measurements, such as sample scale, response 

time, and relatively low temperature measurement resolution, 

transient techniques are being increasingly used to characterize 

the thermal properties of small-scale materials, which are 

widely adopted in micro/nano-electronics. Compared with 

steady-state techniques, transient characterization has 

competitive advantages in response time, precision, and smallscale measurements [17-20]. Of all the transient techniques, 

transient thermoreflectance (TTR) has been extensively used in 

characterizing the thermal/optical properties of thin film

materials [21-25]. Ohsone et al. [23] performed optical 

measurement of thermal contact conductance between thin,

solid films and also established a configuration of frequencydomain thermoreflectance experiment. This experiment was

then modified by Tong et al. [26] to study CNTs as novel 

interface materials. In addition to frequency-domain TTR, 

Lyeo and Cahill [25] used time-domain TTR to measure the 

thermal conductance between highly dissimilar materials. They

concluded that coupling electrons in a metal to phonons in a 

dielectric substrate does not significantly contribute to thermal 

transport at interfaces. Komarov and Raad [24] analyzed the 

performance of the TTR method for measuring the thermal 

conductivities for various materials. 

In this work, we mainly focus on TIMs which could be 

applicable for power electronics packaging applications. 

Narumanchi et al. [27] briefly reviewed the state of the art of 

TIMs in power electronics applications. In automotive power 

electronics, it is critical to have efficient heat removal to keep 

device temperature under limits, assure high reliability and 

lower the cost of components. In a power electronics package, 

the thermal resistance of interface materials depends on both 

the thermal conductivity of the fillers and also the 

conformability to mating surfaces. When a TIM is applied, the 

bondline thickness (BLT) is usually as thin as tens of 

micrometers, and the thermal conductivity of this scale is 

expected to be smaller than its bulk value. Also, because of the 

non-ideal surface contact and adhesion, the interface emerges 

as a significant hindrance to heat removal. Therefore, study of

the thermal conductivity and contact resistance simultaneously 

aids in understanding the impacts from these factors, thus

improving the synthesis of TIMs. In addition, for very low 

thermal resistance materials (< 1 mm2

·K/W), some of the 

conventional steady-state (e.g. ASTM-D5470) and transient 

(e.g. xenon flash) techniques are inadequate. For these reasons, 

we developed a laser-based phase-sensitive TTR (PSTTR) 

technique and performed measurements on different TIMs to 

derive their thermophysical properties. The experimental 

method is briefly introduced and principles of PSTTR are 

presented. Heat transfer modeling and corresponding 

theoretical analysis are then described, along with applicable 

solutions of phase lag used to fit parameters of interest.

Measurement results and discussions are presented along with 

sensitivity and uncertainty analysis.

EXPERIMENTATION

Sample Preparation

We studied four test articles in this work to determine their 

thermophysical properties when used as thin bonding layers. A 

plain 100 μm thick silicon wafer was used for baseline 

measurement and calibration. A variety of commercial and 

advanced TIMs were chosen to synthesis the layered samples. 

The first layered sample we fabricated was composed of Dow 

Corning TC-5022 thermal grease sandwiched between two 100 

μm thick silicon wafers. After cleaning the surface, a small 

quantity of TC-5022 was applied to one wafer, and the second 

wafer was pressed onto the grease and squeezed to cause the 

grease to flow between the two wafers. The samples were

further annealed under elevated temperature and under 

pressure to create the possibly smallest layer of grease. Typical 

grease layer thickness of 60 to 70 μm was achieved, in 

accordance with those of most BLTs of thermal greases. This 

sample represents a standard commercial method of creating 

thermal contact between cold plates and electronic components.

The second layered sample for TIM study was made by 

bonding two plain silicon wafers using Btech thermoplastic 

film (HM-2, from Btech Corp.). The film is a composite of 

high-density graphic fibers mixed with high temperature 

adhesive. Btech thermoplastic film was chosen because the 

highly aligned fibers are intended to provide enhanced out-ofplane thermal conduction between the hot component and the 

cooling media. The sample was assembled similarly to the one 

bonded using Dow thermal grease. A piece of film was placed 

between two 150 μm thick silicon wafers and bonded together 

using force and heat per the manufacturer’s recommendations. 

A Btech material thickness of about 60 μm was achieved.

Among emerging new classes of high-performance bonding 

techniques, diffusion bonding is a promising one in wafer 

bonding as it removes physical interface materials to enhance 

the heat dissipation. The diffusion-bonded silicon samples on 

which measurements were performed in this work were 

synthesized by our collaborators (Delphi). A microscopic 

image of the bondline is shown in Fig. 1, with thickness 

marked for two silicon wafers.

Phase-sensitive transient thermoreflectance

Experiment setup of PSTTR. The configuration of the 

PSTTR technique is presented in Fig. 2. The pump laser is 

modulated using a wheel chopper at a particular frequency, f, 

and then is focused onto the front surface of the sample. The 

absorption of this energy at the front surface generates a 

thermal wave traveling through the sample, inducing 

temperature fluctuation of the same frequency f on the back 

surface. A probe laser is focused to detect the small 

temperature fluctuation.
3

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Fig. 1 Microscopic side view of diffusion-bonded sample; the

thicknesses of the two bonded silicon wafers are shown.

Within a small range of temperature variation, namely, 10 

degrees, the coefficient of thermoreflectance is assumed 

constant and the reflectivity change is linearly proportional to 

temperature change. Thermoreflectance describes a surface’s 

ability to reflect an optical signal and is highly dependent on 

the materials and also the wavelength of the optical signals. A 

photodiode is used to receive the reflected probe laser and then 

the converted electrical signal is transmitted to a lock-in 

amplifier. By comparing it with a reference input from the 

pump laser modulation, the lock-in amplifier extracts the 

amplitude and phase information of the signal at the frequency 

f. Because the amplitude depends on many factors, such as the 

power of the laser heating, laser spot size, and surface 

properties, most of which are not documented in literatures, the 

theoretical predication of the amplitude faces many unknowns 

and uncertainties. Contrarily, the phase of the signal is 

independent of these parameters and only depends on the 

thermal properties of the sample, e.g., the thermal conductivity 

of the materials, thermal conductance of interfaces, etc. Hence,

the phase information of the reflected signal is chosen over the 

amplitude to derive the thermal properties based on the 

corresponding heat transfer modeling.

The apparatus for this technique is also shown in Fig. 2. 

Heating is provided by a diode laser (pump laser) at a 

wavelength of 808 nm and a maximum power of 5W. The 

continuous laser signal is then modulated by an optical chopper. 

The modulation frequency is controlled by a waveform

generator (Picotest G5100A), which also output the same 

frequency into the lock-in amplifier as a reference input. The 

heating laser is focused onto the surface with a spot radius of 

approximately 1.5 mm, yielding a maximum flux of about 2.83 

W/mm2

. Another diode laser of 405-nm wavelength and much 

reduced power of about 5 mW is employed as the probe laser. 

The spot size of the probe laser is about 0.3 mm radius, small 

enough compared with the spot size of pump laser. Therefore, 

the probe laser is simply used to detect the temperature 

variation without introducing a thermal effect to the 

temperature field. A Gallium Phosphide (GaP) photodiode 

(Thorlab DET-25K) is connected to a 20KΩ resistor by 

amplifying the photodiode signal into a lock-in amplifier

(SR850, Stanford Research System). During each 

measurement, a series of frequencies is generated, and then the 

pump-probe process is conducted at each frequency. A 

LabView data acquisition system is used to automatically 

complete the whole measurement.

Among many factors that may affect this experiment, the 

alignment of two laser signals is most critical, as it strongly 

influences the strength of signal into the photodiode. Both the 

pump and probe lasers are mounted on motorized stages, 

ensuring accurate adjustment of each spot. The probe laser spot 

is first fixed and marked using a charge-coupled device (CCD)

camera. The pump laser is then fine-tuned using the motorized 

stages to identify the best alignment by observing the intensity 

readings of the lock-in amplifier. This alignment process is 

usually delicate and difficult due to the small but oscillating 

temperature response on the back surface. In addition, the 

appropriate ratio between the two spot sizes is important for 

the success of the experiment.

Based on a comparison between the photodiode signal and 

a reference input of the modulation frequency, phase reading 

from the lock-in amplifier represents a backward shift from the 

original periodic waveform. Therefore, it is defined as a phase 

lag in this work. This phase lag is not only composed of the 

effect of the thermal transport in the sample, but also that from

the devices and equipment used in the experiment. Therefore, a 

calibration is required so that the systematic and environmental 

effects can be qualitatively determined. Towards this end, the 

experiment is first run at the same frequency series without 

mounting the sample, and the phase lag is recorded as a 

baseline. This baseline phase lag is subtracted from the phase 

lag data acquired from the sample. This systematic phase lag is 

usually consistent when the laser parameters change.

Theory of PSTTR. To extract thermal property 

information from the phase lag data, a transient heat transfer 

model is required to solve the temperature distribution in the 

multi-layer structure upon laser heating. In the simplest case, a 

one-dimensional model is studied first by assuming isotropic 

and temperature-independent thermal properties. The 

governing equation for one-dimensional heat transfer is:

1

α

∂T

∂t = ∂2T∂z2 (1)

where T is the temperature, α is the thermal diffusivity, t is the 

time and z is the spatial coordinate.

113 μm

86μm
4

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Fig. 2 Experimental configuration of the phase-sensitive

transient thermoreflectance technique

Using the separation of variables method and a periodic 

heat source of angular frequency ω, a general solution of Eq. 

(1) is obtained as,

T(t, z) = e−iωt �Ae

(1−i) z

�2α�ω + Be

−(1−i) z

�2α�ω�

= Ae

z

Lpe

i(− z

Lp

−ωt)

+ Be

− z

Lpe

i( z

Lp

−ωt)

, (2)

where the term �2α�ω is defined as the thermal penetration 

depth, Lp, which denotes a length scale over which the thermal 

energy can propagate before getting substantially damped. If 

the thickness is significantly greater than the penetration depth, 

it is then assumed that the sample is relatively thick. By 

adopting a periodic heat flux q0e

-iωt with amplitude q0 and 

frequency ω as the boundary condition at the front surface (z = 

0), Eq. (2) is further derived as:

T(t, z) = q0Lp

√2k

e

− z

Lpe

i( z

Lp

+π

4−ωt)

(3)

where k is the thermal conductivity. A phase lag of �z

Lp � +

π

4� � is identified between heat flux at the front surface and the 

temperature response on the back surface. It is seen from the 

Eq. (3) that the phase lag is only dependent on the thermal 

diffusivity α. Therefore, the phase lag is relatively robust 

compared with the amplitude when deriving the thermal 

properties. The derivation is achieved using a least-square 

fitting technique through the whole frequency range. A typical

fitting plot for a silicon wafer is presented in the Results 

section.

Fig. 3 Schematic of the multi-layer samples measured using 

PSTTR (not scaled).

Three-layer structure. Now we examine multilayer

structures that are common in microelectronics/power 

electronics applications. A typical geometry is shown in Fig. 3.

It contains two solid materials (1 and 3) and one interfacial 

layer (2). The properties of the three layers are indicated by 

subscripts 1, 2, and 3. To theoretically analyze the temperature 

field in a three-layer structure, an axial-symmetric three-layer 

transient heat transfer model is established as: 

1

αi

∂Ti(r,z,t)

∂t = 1

r

∂

∂r �r

∂2Ti(r,z,t)

∂r � + ∂2Ti(r,z,t)∂z2 , (4)

where the subscript i represents the ith layer (i = 1, 2, 3), as 

denoted in Fig. 3. Due to the geometric symmetry of the 

structure, only heat transfer occurring along the r and z

directions is considered, indicated by the coordinate axes in 

this figure. In addition, heat loss from the surface to the

surroundings is assumed to be negligible. Then the boundary 

conditions are as follows:

At z = 0, a periodic heat source of intensity q0 and angular 

frequency ω are used:

q0f(r)e−iωt = −k1

∂T1

∂z ; (5-1)

at z = b3, an insulation boundary condition is applied, due to 

the case that the thickness is large enough and also the Biot 

number is small:

k3

∂T3

∂z = 0; (5-2)

at z = b1, which is interface 1, the energy balance is shown as: 

−k1

∂T1

∂z �

z=b1

= h12�T1(b1) − T2(b1)� = −k2

∂T2

∂z �

z=b1

;(5-3)

The same boundary condition is also applied to interface 2 

at z =b2, 

−k2

∂T2

∂z �

z=b2

= h23�T2(b2) − T3(b2)� = −k3

∂T3

∂z �

z=b2

,(5-4)

where k1, k2, and k3 are the thermal conductivities of the 

respective layers; h12 and h23 are the contact conductance at the 

1–2 interface and the 2–3 interface, respectively. f(r) is the 

axial symmetric heating function that defines the heat flux 

distribution over the surface and is assumed to be uniform to 

simplify the analysis. The surface outside of the heating region 

Solid layer 1

Solid layer 3

Interfacial 

layer 2

z = 0

z = b2

z = b1

z = b

3

d1

d2

d

3

Pump laser

Probe laser

z

r

Pump Laser

Function Generator

Lock-in Amplifier

Multi-mode 

optical fiber

Collimation 

lenses

Lens tube

Modulated 

pump laser

Optical 

chopper

Probe Laser

Reflecting 

mirrors

Photodiode

Modulated 

pump laser Heat 

transfer Probe Laser

Probed 

temperature 

variation

Sample
5

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is insulated because the laser heating is localized and the

geometry along the thickness direction is much smaller than 

that at the other directions.

This equation is solved by using the integral transform 

method [23]. After the Hankel transform and Laplace 

transform are implemented, the governing equation is 

converted as follows: 

∂2wi(λ,z,s)

∂z2 − �λ2 + s

αi

� wi(λ, z, s) = 0, (6)

where λ and s are the variables resulting from the Hankel and 

Laplace transforms, respectively. wi(λ, z, s) is the Hankel and 

Laplace transform of temperature function Ti(r, z, t). Then, the 

general solution for the i-th layer is expressed as:

wi(λ, z, s) = Ã

icosh(ηiz) + B�isinh(ηiz), (7)

where ηi = �λ2 + s

αi

.

The boundary conditions are written as: 

q0

s+iω ∫ f(r) ∞

r=0 ∙ J0(λr)dr = −k1

∂w1

∂z �

z=0

, (8-1)

−k1

∂w1

∂z �

z=b1

= h12(w1 − w2)|z=b1 = −k2

∂w2

∂z �

z=b2

,(8-2)

−k2

∂w2

∂z �

z=b2

= h23(w2 − w3)|z=b2 = −k3

∂w3

∂z �

z=b3

,(8-3)

−k3

∂w3

∂z �

z=b3

= 0, (8-4)

where J0(λr) is the zeroth Bessel function, which represents the 

Hankel transform of the heating function. Coefficients Ãi and 

Bi are solved by substituting the general solution into boundary 

conditions. Then inverse transforms are used to recover the 

temperature distribution in real space. 

Because only the temperature response on back surface is 

of interest, r = 0 and z = b3 are chosen to retrieve the 

temperature distribution on the back surface. Under a highfrequency limit, the solution is simplified as:

T3(0, b3,t) = 4q0

k1�πf

α1 �

∙ exp �− �d1�πf

α1

+ d2�πf

α2

+ d3�πf

α3

��

exp�i�

π

4+d1�πfα1

+d2�πf

α2

+d3�πf

α3

−ωt��

⎣

⎢

⎢

⎡ 1+�(kρc)2

(kρc)1

+�(kρc)3

(kρc)1

+�(kρc)3

(kρc)2

+(1−i)

�πf(kρc)2

h12 +(1−i)

�πf(kρc)3

h12 +

(1−i)

�πf(kρc)3

h23 +(1−i)�(kρc)2

(kρc)1

∙

�πf(kρc)3

h23 +(1−i)2�πf(kρc)2h12 ∙

�πf(kρc)3

h23 ⎦

⎥

⎥

⎤

,

(9)

where d1 = b1, d2 = b2 - b1 and d3 = b3 - b2, as seen in Fig. 3, 

denote the thickness of each layer. Thermophysical properties 

in each layer are summarized into one term �(kρc)i, i = 1, 2, 3. 

This expression is defined as thermal effusivity, which is a 

measure of a material’s ability to exchange thermal energy 

with its surroundings. Given that the thermal resistance R is the 

reciprocal of the thermal conductance h, the phase lag in the 

high-frequency limit can be then extracted as:

∅ = π

4 + d1�πf

α1

+ d2�πf

α2

+ d3�πf

α3

+

tan−1

⎣

⎢

⎢

⎢

⎢

⎡ �

�πf(kρc)2∙R12+�πf(kρc)3∙R12+�πf(kρc)3∙R23+

�(kρc)2

(kρc)1

∙�πf(kρc)3∙R23+2�πf(kρc)2∙R12∙�πf(kρc)3∙R23�

⎝

⎛

1+�(kρc)2

(kρc)1

+�(kρc)3

(kρc)1

+�(kρc)3

(kρc)2

+�πf(kρc)2∙R12+�πf(kρc)3∙R12+

�πf(kρc)3∙R23+�(kρc)2

(kρc)1

∙�πf(kρc)3∙R23 ⎠

⎞

⎦

⎥

⎥

⎥

⎥

⎤

(10)

Eq. (10) expresses the phase lag at the back surface and is 

related to several key parameters, such as the thermophysical 

properties of each layer and also the contact resistances, which 

are of particular interest. With the theoretical phase lag and 

experimental data, the thermophysical properties can be 

precisely estimated using a multi-parameter fitting method. 

Although the phase lag (Eq. (10)) is derived based on a 

three-layer heat transfer model, it is applicable to derive the 

temperature distribution in both two-layer and single-layer 

structures, with necessary assumptions for the thermal and 

physical properties. Note that in Eq. (10), if R12 and R23

approach 0, meaning an absence of interfaces, and all 

thermophysical properties are set to be identical, this equation 

reduces to the following form:

∅ = π

4 + �πfα1

(d1 + d2 + d3), (11)

which is in exactly the same form as the phase lag in Eq. (3).

Eq. (10) is also used to derive a solution for a two-layer 

structure. By applying similar assumptions that the contact 

resistance R12 is 0 and solid layer 1 and bonding layer 2 

possess identical thermophysical properties, namely, (kρc)1 = 

(kρc)2, Eq. (10) further reduces to the following expression:

∅ = π

4 + �πfα1

(d1 + d2) + d3�πf

α3

+

tan−1 � ��πf(kρc)3∙R23�

�1+�(kρc)3

(kρc)1

+�πf(kρc)3∙R23�

�. (12)

The solution of a two-layer structure is useful when 

studying a direct-bonded sample, which usually contains no 

physical bonding material, only a pure bond line.

This series of phase lag solutions for single-layer (Eq. (11)), 

two-layer (Eq. (12)) and three-layer (Eq. (10)) structures

inspires us to conduct an in-depth study of heat transfer in a 

generic multi-layer structure. It is observed from these 

equations that all three solutions follow a certain regularity of 

contributions from different materials. A (π/4) term appears in 

all three equations, which represents an intrinsic phase lag

caused by absorption of heat on the front surface, regardless of 

materials. Terms in the form of b/lp indicate the phase lag 

caused by thermal wave propagation inside each layer. 

Contributions of the interfaces and thermophysical properties

are included in the inverse tangential function. Following the 

same geometrical setting and analogous boundary conditions, a 

general N-layer model can be established and solved. The Nlayer model solution provides a useful reference when a 
6

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complicated multi-layer sample is studied using optical heating 

and sensing techniques, such as PSTTR and laser flash. More 

details and derivations will be discussed in another paper.

RESULTS AND DISCUSSIONS

Single materials

To validate the experimental setup and confirm the 

accuracy of the technique, it is necessary to measure materials

with documented properties. A single silicon wafer was first 

tested as a standard material because its thermal and physical 

properties are well studied. Silicon wafers of different 

thicknesses (100, 120, 150, 170, 270, and 280 μm) were tested

using PSTTR. Typical phase lag–frequency data points are 

plotted in Fig. 4, in which a theoretical line is also added. As 

shown in Eq. (3), the phase lag is linearly dependent on the 

term b/Lp. with an intercept of –π/4. Therefore, in Fig. 4, if a 

normalized frequency is chosen as the x axis, measured points 

from silicon wafers of varied thicknesses all converge to close

to the theoretical linear profile. If the thickness is too small so 

that the penetration depth is comparable or larger than the 

thickness, the front side phase lag and traveling wave phase lag 

both approaches 0, resulting an overall phase lag of ~ 0. Only 

when the thickness is large, the total phase lag is quantified as 

(π/4+b/Lp). [26] Therefore, to satisfy the thick-sample 

assumption, frequencies are carefully chosen to ensure the 

thermal penetration depth is smaller than the thickness. Usually 

the applicable frequency region is determined when the ratio 

b/lp is greater than 0.8, which is defined as the high-frequency 

limit. The frequency determined by this limit assures that the 

phase lag at the front surface approaches π/4 and the

contribution from the traveling thermal wave is b/lp [23, 26].

From Fig. 4, the region of b/lp > 1.0 is intentionally chosen for 

global fitting. The optimal agreement between the 

experimental data and the theoretical solution yields the best 

value for the thermal diffusivity for the tested silicon wafer. 

Taking a silicon wafer of 100 μm thickness for instance, the 

thermal diffusivity is fitted to be about 7.9 × 10-5 m2

/s. The 

density and specific heat of silicon are 2,230 kg/m3 and 712 

J/(kg·K), respectively, [28] thus, the thermal conductivity is 

calculated to be 131 W/(m·K), in good agreement with the

generally documented value of 135 W/(m·K). [23] If the 

thickness varies, the derived thermal diffusivity does not show 

a significant change because the normalized frequency–phase 

curves at different thicknesses actually converge to the 

theoretical profile. Measurement results and parameters 

adopted in the fit are listed in Table 1, along with uncertainties 

for the fitted parameters, such as thermal conductivity, k, and 

thermal diffusivity, α.

Fig. 4 Plot of experimental phase lags as a function of 

normalized frequency for plain silicon wafers of 

different thicknesses. The theoretical phase lag profile 

is also added for comparison.

Table 1. Parametric values for three different materials 

measured in this work using PSTTR. Uncertainties of fitted 

values are marked. 

Parameters Silicon 

wafer TC-5022 Btech 

HM-2

Total Thickness

(μm) 100 270 380

BLT

(μm) 70 60

Density

(kg/m3) 2,330 3,230 1,520

Specific heat

(J/(kg·K)) 712 251 1,010

Thermal 

conductivity

(W/(m·K))

131 ± 17.00 3.41 ± 

0.34

37.53 ± 

6.76

Thermal 

diffusivity

(×10-5 m2/s)

7.90 ±

1.00

0.42 ± 

0.04

2.44 ± 

0.44

Contact resistance

(mm2·K/W)

8.74 ± 

3.06

3.06 ± 

1.07

Total thermal 

resistance

(mm2·K/W)

37.03 ± 

6.40

7.49 ± 

1.87

Thermal grease TC-5022 

As a predominant TIM use in the automotive industry, thermal 

grease has been widely studied. However, the ASTM D5470

technique or the transient laser flash technique can only 

provide the overall interfacial thermal resistance without 

distinguishing the effects from the interface material and 

contacting surfaces. Therefore, an in-depth study to understand 

the thermal properties of each component would aid in 

improving the performance of thermal grease and the synthesis 

of other types of TIMs. The thermal grease measured in this 

work is Dow Corning TC-5022 material, and the fabrication 

details of the sample are introduced in a prior section. The 

-4

-3

-2

-1

0

0 1 2 3 4

Theoretical

100 

120

150

170

270

280

Phase lag (radian)

Normalized frequency

Theoretical phase 

100 μm

120 μm

150 μm

170 μm

270 μm

280 μm
7

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bound silicon wafers are studied as well, using PSTTR as 

stated above. Their geometrical, physical, and thermophysical 

properties are recorded and then used in the data analysis of 

three-layer sample measurement. The overall thickness is 

slightly different from spot to spot, varying from 60 to 70 μm. 

As analyzed above, the silicon-grease-silicon composite 

structure is a three-layer model, and Eq. (10) gives the phase 

lag in the high frequency region. In addition, Eq. (9) shows 

that the temperature oscillation at the back surface varies as 

�− �d1�πf

α1

+ d2�πf

α2

+ d3�πf

α3

�� , and it strongly depends on 

the thermophysical properties and also the frequencies. 

Therefore, if the modulation frequency is increased, the 

temperature response on the back surface will decrease

exponentially. This is also observable from the lock-in

amplifier readings. Thus, to assure a signal strong enough to 

suppress the environmental disturbance, the frequency range 

chosen is from 2 to 4 kHz. In Fig. 5, typical phase lag data for

TC-5022 is plotted out against the normalized frequency. The 

results from theoretical modeling are also added for 

comparison. The x-axis is the normalized frequency, which 

summarizes the traveling wave contribution in each layer. As 

seen, the measured data points show some oscillation but are 

still very close to the theoretical results. Because the PSTTR 

technique considers overall interfacial thermal resistance as a 

combined effect from discrete components, there are several 

undetermined interface material properties, such as density, 

specific heat, thickness, and thermal diffusivity, as indicated in

Eq. (10). Some properties are documented and are used as 

constants through the fitting process, while some other 

properties, such as thermal conductivity, thermal diffusivity,

and contact resistance, remain unknown and need to be 

determined. When implementing the multi-parameter fitting 

method, these to-be-determined properties are set to change

within certain ranges until a set of values that gives the best fit 

between the experimental and theoretical data is identified. For

the TC-5022 measurement shown in Fig. 5, the thermal 

diffusivity is 5.44 ×10-6 m2

/s, and the contact resistance of the 

silicon–TC-5022 interface is 8.19 mm2

·K/W, which represents 

the single interfacial thermal resistance only. By adopting a 

density of 3,230 kg/m3 and a specific heat of 251 J/(kg·K), the 

thermal conductivity of TC-5022 is calculated to be 4.41 

W/(m·K). Because the heat flow is primarily along the 

thickness direction, based on thermal circuit series assumptions, 

the overall interfacial thermal resistance is 32.9 mm2

·K/W. It is 

then concluded that about 50% of the thermal resistance is 

caused by thermal transport within the material, and the other 

50% is from the scattering at the contact surfaces. This 

measured interfacial thermal resistance is greater than prior 

measurements in our group using the ASTM method D5470

test method - which was about 25 mm2

·K/W for 70 μm thick 

thermal grease layer. [27]. A probable reason for the difference 

is because the PSTTR measurement is very localized at a small 

area of about 1- to 2-mm radius and ASTM D5470 is 

conducted over a much larger area. Therefore, the thermal 

resistance measured by the ASTM D5470 test method better

reflects a region-averaged thermal performance, but the actual 

resistance still varies from spot to spot. In order to acquire the 

thermal resistance distribution of the interface, the PSTTR

technique should be used to scan the whole surface area. 

Another possible reason is that we keep applying an external 

pressure when implementing the ASTM method, which

improves the surface contact. The sample tested by PSTTR is 

mounted in a free condition without exterior pressure. Hence,

the surface contact may be affected by the continuous laser 

heating. However, PSTTR has presented an insight into the 

interface and reveals that the thermal grease material and 

contact surfaces induce almost equal impedance to the heat 

flow. In addition, to eliminate random error from a single 

measurement, multiple measurements are performed, and the 

averaged fitted values of the selected parameters are listed in 

Table 1. 

Btech thermoplastic film (HM-2)

Btech thermoplastic film is another TIM that uses highly 

aligned high-density fibers to conduct heat efficiently. Since

the fibers are aligned in the thickness direction, heat transfer is 

significantly enhanced in the thickness/out-of-plane direction. 

The overall thickness of the bonded sample is about 370 μm. 

Measurements of the Btech thermoplastic film-bonded sample 

are depicted in Fig. 6. The theoretical results are also plotted.

The fitted thermal diffusivity is 1.38 × 10-5 m2

/s, and the 

thermal conductivity is calculated to be 21.15 W/(m·K), when 

a density of 1,520 kg/m3 and a specific heat of 1,010 J/(kg·K) 

are used. The contact resistance is determined to be 2.58 

mm2

·K/W. The overall thermal resistance of the thermoplastic 

layer is calculated to be 8.94 mm2

·K/W, about 60% of which is 

from the contact resistance. The Btech sample is also studied 

using the xenon flash technique. The overall interface thermal 

resistance was measured at around 6 mm2

·K/W, close to the 

derived values in this work. To eliminate the uncertainty from 

individual measurements, PSTTR was conducted repeatedly at 

different positions.

Fig. 5 Experimental and theoretical phase lags as a function of 

normalized frequency for a silicon-grease-silicon

multilayer sample.

The out-of-plane bulk thermal conductivity of the 

thermoplastic layer was determined to be around 20 to 50 

W/(m·K). These values are much higher than most polymers 

and semiconductors, but are still more than one order of 

magnitude lower than the out-of-plane thermal conductivity of 

-6

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

1.5 2 2.5 3 3.5 4

Theoretical phase lag

Experimental phase lag

Phase lag (radian)

Normalized Frequency
8

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HM-2, which is about 700 W/(m·K). This significant reduction 

is probably caused by the non-ideal bonding quality. The 

existence of misalignments and imperfections strongly hinders

the phonon transport along the thickness direction and causes

lower thermal conductivity; however, the total interfacial 

thermal resistance of Btech HM-2 thermoplastic film is still 

much lower than that of the thermal grease. If the bonding 

process is carefully executed to maintain ideal alignment of the 

graphite fibers, the thermal resistance could be further 

decreased. This predication makes Btech thermoplastic film an

excellent candidate for highly efficient heat removal. Averaged

fitted values for key parameters, such as thermal conductivity 

and contact resistance are derived based on results from 

multiple measurements, as listed in Table 1.

Diffusion-bonded sample

Diffusion bonding is a novel process that bonds materials 

without additional intermediate layers. It can be used to bond 

both metals and nonmetals. Among all applicable materials, 

silicon is the most established material up to now. The 

diffusion-bonded sample in this work was provided by our 

collaborators Delphi, and uses two pre-processed silicon 

wafers. The thickness is measured to be 200 μm after bonding. 

To achieve optimal bonding quality, a layer of aluminum about 

2 μm thick is sputter coated on each mating surface. Because 

diffusion bonding is based on atomic interactions, the bonding 

quality is assumed much improved over conventional bonding 

materials. In this work, because two thin layers of aluminum 

are coated, we then consider the interface to be an Al–Al 

interface. Together with the two silicon wafers, the bonded 

sample is described as a four-layer structure, which includes 

four layers of material (silicon, aluminum, aluminum, silicon)

and three contact interfaces (Si–Al, Al–Al, Al–Si). The fourlayer model is analogous to the three-layer model discussed 

above, and theoretical solutions are acquired following the 

same method.

Fig. 6 Experimental and theoretical phase lags as a function of 

normalized frequency for a sample bonded with Btech 

HM-2 thermoplastic film.

The phase lag based on four-layer modeling is much more 

complicated than Eq. (10). Similar to the three-layer heat 

transfer model, the constant π/4 term and phase lags from the

thermal wave traveling in each layer remain the same. 

However, the number of interfaces brings greater complexity 

into the solution. Nevertheless, patterns related to the 

effusivities and resistances are noticeable, similar to that 

indicated in the phase lag solutions in the theoretical modeling

section. A four-layer solution is then validated by its 

reducibility to Eq. (10), Eq. (12), and Eq. (11) using

appropriate assumptions. 

With a four-layer phase solution, the multi-parameter 

fitting method is performed. Both experimental and theoretical 

phase lags are presented in Fig. 7. Based on the fit, the thermal 

resistance is determined to be 0.53 mm2

·K/W. To be more 

specific, the contact resistance between silicon and aluminum 

surfaces is about 0.08 mm2

·K/W. According to work reported 

on solid interfaces, room-temperature contact resistances 

between metals and dielectrics are about 0.01 to 0.1 mm2

·K/W.

[29, 30] In addition, the thermal resistance of the 2-μm

aluminum coating is less than 0.01 mm2

·K/W, which is 

negligible compared to that of other components. The Al–Al

interface contact resistance is fitted to be 0.34 mm2

·K/W, 

meaning that over 60% of the thermal resistance is caused by 

this interface. The contact resistance is mainly caused by 

phonon/electron scattering at the interface and also the ambient 

imperfections, such as voids and dislocations. Because the 

aluminum layer is sputter coated, the adhesion is optimal. In 

addition, the coated aluminum layer has ultra-fine and highly 

uniform surface features. In comparison, when the two silicon 

layers are bonded at elevated temperature and additional 

pressure, the surfaces do not adhere as well as a sputter-coated 

surface. Therefore, the resistance from an Al–Al interface

emerges as stronger impedance to the heat flow. Upon several 

measurements, the averaged values for the two contact 

resistances are presented in Table 2. The interfacial thermal 

resistance of the diffusion-bonded silicon wafers is 

impressively low compared with the thermal resistances in 

Table 1.

Table 2. Parameters of diffusion-bonded sample.

Parameters Value

Total Thickness (μm) 200

Bondline thickness (μm) 4.00

Density of Aluminum (kg/m3) 2,700

Specific heat of Aluminum

(J/(kg·K)) 900

Thermal conductivity of 

Aluminum

(W/(m·K))

205

Thermal diffusivity of 

Aluminum (×10-5 m2/s) 8.40

Al–Si contact resistance

(mm2·K/W) 0.06

Al–Al Contact resistance

(mm2·K/W) 0.33

Overall thermal 

resistance (mm2·K/W) 0.47

-6

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

2 2.5 3 3.5 4

Theoretical phase lag

Experimental phase lag

Phase lag (radian)

Normalized Frequency
9

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Fig. 7 Experimental and theoretical phase lags as a function of 

normalized frequency for the diffusion-bonded sample.

Measurement sensitivity

To achieve effective measurements, a study of sensitivity of 

the output signal to parameters is necessary. The greater the 

change in output signal due to changes in particular parameters

is, the more accurately the parameter is determined. Graphic 

presentations of the sensitivity of critical parameters for the 

samples measured are shown in Fig. 8. For all three plots in 

Fig. 8, in addition to the experimental and theoretical curves,

several other curves obtained by varying relevant parameters to 

certain levels are also included. Fig. 8(a) shows how much the 

phase lag changes from the best fit curve upon ±10% change in 

thermal diffusivity. Distinct deviations are observed in this 

figure when thermal diffusivity is either enhanced or reduced 

by 10%. This suggests that the phase lag is sensitive to thermal 

diffusivity and the fitted value of thermal diffusivity is accurate 

enough. It is also seen that when the frequency increases, the 

deviation from the theoretical curve is greater. This suggests 

that the sensitivity is also related to the frequency. If a higher 

sensitivity needs to be achieved, an appropriate frequency 

range is required. The sensitivity curves of TC-5022 and Btech 

HM-2 are shown in Figs. 8(b) and 8(c), respectively. Using

variations of 20%, the thermal conductivity and thermal 

resistance show drastically different influences on the system 

sensitivity. The curves with ±20% thermal resistance are very 

close to the best fit curve, while curves with ±20% thermal 

conductivity significantly depart from the best fit curve. Insets 

in both Figs. 8(b) and 8(c) show this difference more clearly. 

As stated, it is seen that the deviation from the theoretical 

curves upon certain variations of the parameters is not constant 

through the frequency range. Therefore, if we understand how 

sensitivity is qualitatively related to the frequency, it is 

instructive for us to determine the proper frequency to be used 

in the measurements. The sensitivity of a measurement output

to a specific parameter is quantitatively expressed as the partial

derivative of the function over that parameter, namely, df/db, 

in which f is the output signal and b is the experimental 

parameter.

For single silicon wafer materials, based on Eq. (3), the 

sensitivity of the phase lag on the thermal diffusivity is 

expressed as:

|∆∅| = ��

d∅

dα� ∙ ∆α� = �

b·�πf

2 α−3

2 ∙ ∆α� (13)

Fig. 8 (a) Calculated phase lag curve changes for the single 

silicon wafer data on ±10% changes in thermal 

diffusivity α around the best fit value; (b) Calculated 

phase lag curve changes for TC-5022 bonded sample 

upon ±20% changes in bulk thermal conductivity, k, and 

contact resistance, R, around the best fit value; (c) 

Calculated phase lag curve changes for Btech HM-2 

bonded sample upon ±20% changes in bulk thermal 

conductivity, k, and contact resistance, R, around the 

best fit value. Insets in (b) and (c) are partial enlarged 

images to more distinctly show the deviations from best 

fit curves upon certain changes in the fitted parameters.

-4

-3.5

-3

-2.5

-2

-1.5

1 1.5 2 2.5 3

Theoretical phase lag

Experimental phase lag

Phase lag (radian)

Normalized Frequency

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6

Theoretical phase lag

Experimental phase lag

r12*0.8

r12*1.2

k2*0.8

k2*1.2

Phase lag (radians)

Normalized frequency

(c) Btech HM-2

R12×80%

R12×120%

k

2

×120%

k

2

×80%

-4.8

-4.65

-4.5

-4.35

3 3.05 3.1 3.15 3.2

-6

-5

-4

-3

-2

1.5 2 2.5 3 3.5 4

Theoretical phase lag

Experimental phase lag

R12*0.9

R12*1.1

k2*0.8

k2*1.2

Phase lag (radians)

Normalized frequency

R12×80%

R12×120%

k

2

×120%

k

2

×80%

(b) TC-5022

-4.95

-4.8

-4.65

-4.5

3 3.05 3.1 3.15 3.2

-3

-2.5

-2

-1.5

-1

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

Theoretical phase lag

Experimental phase lag

-3

-2.5

-2

-1.5

-1

Phase lag (radian)

Normalized frequency

α×110%

d = 100 μm α×90%

(a) Single silicon wafer
10 

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Fig. 9 Absolute values of phase changes in a silicon wafer as a 

function of frequency with respect to a 10% change in 

thermal diffusivity and thickness. 

So, when the thermal diffusivity is set to vary by 10%,

namely, ∆α is α ×10%, the change in the phase lag is a 

function of frequency as described by Eq. (13). Greater change 

in phase indicates it has greater sensitivity to the thermal 

diffusivity α. Therefore, from Fig. 9, the phase lag for a single 

silicon wafer is more sensitive to thickness than to the thermal 

diffusivity. The sensitivity of phase lag to both parameters 

increases with frequency.

For both thermal grease and Btech thermoplastic film 

measurements, three-layer heat transfer modeling is applied 

and a multi-parameter fitting technique is used to find a set of 

parameters that yield the best fit. Because multiple parameters 

are of interest in three-layer samples, the sensitivity of the 

phase lag to each parameter is investigated separately. Because 

of the structural symmetry, the two contact resistances are 

actually interchangeable, so the sensitivities of phase lag to 

both R12 and R23 are equal. The phase change in absolute value 

upon a 10% change of these parameters is plotted in Fig. 10. 

Because of the correlation between thermal conductivity and 

thermal diffusivity, only the sensitivity curve to thermal 

conductivity is shown. It is clearly observed that when the 

modulation frequency increases, the phase change is more 

sensitive to thermal conductivity than to contact resistance. In 

addition, the sensitivities to both contact resistances are 

identical, as stated above.

Uncertainty analysis

When conducting the PSTTR experiment, environmental 

noise and disturbance may introduce errors into the phase 

measurement. To further estimate the uncertainty in the 

parameters due to the errors in phase measurement, error 

propagation equation is employed here, as defined below: 

∆f

f = 1f ∙ � ∂f∂xi

∙ ∆xi� (14) 

Therefore, for a single silicon wafer, if the error in thermal 

diffusivity is of concern, it is then modified into a function of 

phase, 

∆α

α = 1α ∙ �∂α∂∅ ∙ ∆∅� = � 2

∅−π

4

∙ ∆∅� (15) 

Fig. 10 Absolute values of phase changes of (a) TC-5022 and 

(b) Btech HM-2 bonded sample as a function of 

frequency with respect to a 10% change in thermal 

conductivity k and contact resistance R. 

Here, ∆φ is the error in phase readings from the lock-in 

amplifier; which is about 5 degrees (0.08 radians). Hence, the 

percentage error in the derived thermal diffusivity is estimated 

to be from 8% to 19%, depending on the frequency range 

chosen for measurement. At higher frequencies, the percentage 

error approaches the lower end of about 8%, meaning that high 

frequency reduces the uncertainty. This is also supported by 

the sensitivity analysis in the previous section. For a single 

silicon wafer, the sensitivity of phase measurement to thermal 

diffusivity gets greater when frequency increases, as shown in 

Fig. 9. Therefore, high frequency is required in PSTTR 

measurement, not only to derive the theoretical solutions, but 

also to ensure high sensitivity and low measurement 

uncertainty. Because the uncertainty changes with frequency 

selected in measurement, a mean uncertainty of 13% is 

selected for thermal diffusivity α for a single silicon wafer. To 

further derive the uncertainty for thermal conductivity, errors 

in density ρ and specific heat cp are required. Because silicon 

is a well-studied material, the errors for density and specific 

heat are assumed to be 1%. Therefore, the uncertainty for the 

thermal conductivity k based on error propagation theory is 

13%.

For thermal grease TC-5022 and Btech HM-2 thermoplastic 

film, uncertainty analysis in the thermal conductivity k and 

0

0.05

0.1

0.15

0.2

0.25

0 2000 4000 6000 8000 1 104

Thermal diffusivity

Thickness

Phase change (radian)

Frequency (HZ)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 500 1000 1500 2000 2500 3000 3500

 k2 

 R12 

 R23 

Phase change (radian)

Frequency (HZ)

k

2 

R12

R23

(b) Btech HM-2

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 500 1000 1500 2000 2500 3000 3500

k2 

R12 

R23 

Phase change (radian)

Frequency (HZ)

k

2 

R12

R23

(a) TC-5022
11

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thermal resistance R is conducted using the same methodology. 

Details are not included here. Following the same process for 

thermal grease TC-5022, the error for thermal conductivity is 

determined to be 10% and that for contact resistance is 35%. 

Therefore, the uncertainty for overall thermal resistance is 

about 17%. For Btech HM-2 thermoplastic film, the error for 

thermal conductivity, contact resistance, and overall thermal 

resistance are 18%, 35%, and 25%, respectively. Uncertainty 

values for these particular parameters are also indicated after 

the “±” symbols in Table 1. The comparison of uncertainties 

for different parameters indicates that contact resistance 

contains larger uncertainty than thermal conductivity because 

the measurement sensitivity to contact resistance is lower, as 

analyzed above.

CONCLUSION

The PSTTR technique is applied to study the thermal 

properties of various types of TIMs. A phase lag–frequency 

profile is obtained, and then a multi-parameters fitting process 

is employed to find the targeted parameters by identifying the 

best fit between the experimental data and theoretical 

calculations. The TIMs studied in this work include a 

conventional thermal grease (TC-5022), Btech HM-2 

thermoplastic film, and diffusion-bond silicon wafers. While 

traditional techniques such as ASTM D5470 and laser flash are

not capable of differentiating sources of thermal resistance 

within the interfacial layer, or for measuring thermal 

resistances below 1 mm2

·K/W, PSTTR provides valuable 

information to understand the interface thermal resistance by 

deriving both the bulk thermal conductivity of the material 

itself and thermal resistance of the surfaces in contact 

simultaneously. Using the PSTTR measurements, the bulk 

thermal conductivity of Dow Corning’s TC-5022 thermal 

grease (70–75 μm BLT) was 3 to 5 W/(m∙K), and the contact 

resistance was 5 to 10 mm2

·K/W. Due to the nature of thermal 

grease, the thermal conductivity from fillers can be further

improved to reduce the interfacial thermal resistance. For 

Btech HM-2 thermoplastic material (45–80 μm BLT), the bulk 

thermal conductivity was from 20 to 40 W/(m∙K), and the 

contact resistance was about 2 to 5 mm2

·K/W. Because the 

Btech thermoplastic film is synthesized from highly aligned 

graphite fibers, most of the impedance to heat flow comes from 

surface contact. A sample fabricated using high-thermalperformance diffusion bonding was also measured in this work. 

Compared with samples prepared using interfacial materials, 

the thermal resistance of the diffusion-bond sample is lower 

than 1 mm2

·K/W, varying from 0.3 to 0.6 mm2·K/W. While

there are metal–metal and metal–dielectric interfaces, most of 

the thermal resistance is from the Al–Al interface, the contact 

resistance of which is about one order of magnitude greater 

than that of the Al–Si interface. Because the aluminum layer is 

sputter-coated, adhesion between aluminum and silicon is 

excellent compared with the bonding quality of an Al–Al

interface. Comparison among these TIMs implies that 

diffusion bonding is the most promising technique that causes

the lowest thermal resistance to heat flow. The thermal 

performance of thermoplastics is also very good. Prior work 

[27] has shown that when the thermal resistance of the 

interface materials is below 5 mm2

·K/W, they will stop being a 

bottleneck to heat removal in most power electronics 

packaging applications. While the thermal performance of the 

diffusion-bonded interface is outstanding (< 1 mm2

·K/W), 

thermoplastics are also very good potential candidates for 

application in advanced low-resistance power electronics 

packaging configurations. 

ACKNOWLEDGMENTS

The authors would like to acknowledge the support 

provided by Susan Rogers and Steven Boyd, Technology 

Development Managers for Advanced Power Electronics and 

Electric Motors, Vehicle Technologies Office, U.S. 

Department of Energy Office of Energy Efficiency and 

Renewable Energy. The authors would like to acknowledge 

Doug DeVoto and Mark Mihalic (NREL) for synthesizing the 

bonded samples based on the Btech material, Jay Browne 

(Btechcorp) for providing the thermoplastic material, as well as 

Ralph Taylor (Delphi) for providing the diffusion-bonded 

sample.

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